Dylan earns money mowing lawns. The amount of money, in dollars, he earns varies as the number of lawns he mows. When he mows 6 lawns, he earns $72.

Answer: a. To shift the graph of f(x) downward 5 units, we subtract 5 from the function: f(x) - 5. To shift it left 3 units, we replace x with x + 3: f(x + 3) - 5. To stretch it vertically by a factor of 4, we multiply the entire function by 4: 4[f(x + 3) - 5]. Finally, to reflect it about the x-axis, we take the negative of the function: -4[f(x + 3) - 5]. Therefore, the equation of the new function g(x) is:

g(x) = -4[1/2^(x+3) - 5]

b. To find the y-intercept, we set x = 0 in the equation of g(x):

g(0) = -4[1/2^(0+3) - 5] = -4[1/8 - 5] = -4[-39/8] = 195/2

Therefore, the y-intercept is (0, 195/2).

c. The domain of g(x) is all real numbers, since there are no restrictions on x.

d. To find the range of g(x), we first observe that the function is decreasing and asymptotic to y = -5 as x approaches infinity. This means that the range of g(x) is all real numbers less than or equal to -5.

Step-by-step explanation:

Answer:

C) 69

Step-by-step explanation:

23 x 6 ÷ 2 =69feet2

ok!

Answer:

So g would be 15.

The value of the functions are;

f(3) = - 3

g(5) = -77

A function can be defined as an equation or expression hat shows the relationship between two variables.

These variables are termed;

From the information given, we have that;

f(x) = -5x + 2

g(x) = -3x²- 2

To determine the function, f(3), and g(5), we have to substitute the value of x as 3 in the function f(x) and the value of x as 5 in the function g(x).

We have;

f(3) = -5(3) + 2

expand the bracket

f(3) = - 13

For the second function;

g(5) =  - 3(5)² -2

g(5) = -77

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Answers:

[tex]\text{Derivative: } \ \ \frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\ \text{Tangent line at (1,1) is: } \ y = -32x + 33\\\\[/tex]

==========================================================

Work Shown:

Let's determine the derivative dy/dx.

Part 1

[tex]26x^{10} + 6x^{26}y+y^7 = 33\\\\ \frac{d}{dx}(26x^{10} + 6x^{26}y+y^7) = \frac{d}{dx}(33)\\\\ \frac{d}{dx}(26x^{10}) + \frac{d}{dx}(6x^{26}y)+\frac{d}{dx}(y^7) = 0\\\\ 10*26x^{10-1} + \frac{d}{dx}(6x^{26})y+(6x^{26})*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\[/tex]

Part 2

[tex]260x^{9} + 26*6x^{26-1}y+6x^{26}*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\ 260x^{9} + 156x^{25}y+6x^{26}*\frac{dy}{dx}+7y^6\frac{dy}{dx} = 0\\\\ 260x^{9} + 156x^{25}y+(6x^{26}+7y^6)\frac{dy}{dx} = 0\\\\ (6x^{26}+7y^6)\frac{dy}{dx} = -260x^{9} - 156x^{25}y\\\\ \frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\[/tex]

There are many other possible ways to express the dy/dx expression.

GeoGebra and WolframAlpha are two useful tools to help verify the answer. Make sure you use the CAS mode in GeoGebra.

-------------------------------------------

Part 3

Now that we know dy/dx, we can determine the slope of the tangent at any point (x,y) on the implicit function curve.

Plug in x = 1 and y = 1.

[tex]\frac{dy}{dx} = \frac{-260x^{9} - 156x^{25}y}{6x^{26}+7y^6}\\\\ \frac{dy}{dx} = \frac{-260(1)^{9} - 156(1)^{25}(1)}{6(1)^{26}+7(1)^6}\\\\ \frac{dy}{dx} = \frac{-260(1) - 156(1)(1)}{6(1)+7(1)}\\\\ \frac{dy}{dx} = \frac{-260 - 156}{6+7}\\\\ \frac{dy}{dx} = \frac{-416}{13}\\\\ \frac{dy}{dx} = -32\\\\[/tex]

The slope of the tangent line at (1,1) is m = -32.

-------------------------------------------

Part 4

Apply the point-slope formula to determine the tangent line.

[tex]m = -32 = \text{ slope}\\(x_1,y_1) = (1,1) = \text{the point the tangent line goes through}[/tex]

So,

[tex]y - y_1 = m(x - x_1)\\\\y - 1 = -32(x - 1)\\\\y - 1 = -32x + 32\\\\y = -32x + 32 + 1\\\\y = -32x + 33\\\\[/tex]

Answer:

Here, given

present population = 20000

according to question,

population gets double every 34 years

i.e P = 20000 × 2

= 40000

now,

P = 40000

T = 68-34 = 34

ie, again p is double

so, P = 40000×2

= 80000

Hence, the population after 68 years from now is 80000

If the temperature is read every 12 hours, then the eighth temperature reading will be taken at 11.15 pm three days after the first reading.

Temperature is a measure of the degree of hotness or coldness of a substance or object, typically measured using a thermometer in degrees Celsius or Fahrenheit.

If the temperature is read every 12 hours, then the time interval between two consecutive temperature readings is 12 hours.

To find the time of the eighth temperature reading, we need to add 12 hours for each of the previous seven temperature readings:

First reading: 11.15 am

Second reading: 11.15 am + 12 hours = 11.15 pm

Third reading: 11.15 pm + 12 hours = 11.15 am (next day)

Fourth reading: 11.15 am (next day) + 12 hours = 11.15 pm (next day)

Fifth reading: 11.15 pm (next day) + 12 hours = 11.15 am (two days after the first reading)

Sixth reading: 11.15 am (two days after the first reading) + 12 hours = 11.15 pm (two days after the first reading)

Seventh reading: 11.15 pm (two days after the first reading) + 12 hours = 11.15 am (three days after the first reading)

Eighth reading: 11.15 am (three days after the first reading) + 12 hours =

11.15 pm (three days after the first reading)

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Solution is in da attachment mate!! :D

Step-by-step explanation:

that is a college question ?

x = cost of a ham sandwich

y = cost of a turkey sandwich

2x + 3y = 29

3x + 2y = 31

let's multiply the first equation by 3, abd the second equating by -2, and then we add them :

6x + 9y = 87

-6x - 4y = -62

------------------------

0 5y = 25

y = 25/5 = $5

let's use the original first equation to get x (but we could use also the second equation, it does not matter).

2x + 3×5 = 29

2x + 15 = 29

2x = 14

x = $7

each ham sandwich costs $7.

each turkey sandwich costs $5.

Answer: Ax+By=C This is the formula

Answer:

A maybe

Step-by-step explanation: sorry if wrong

a. There are three N's in PENNSYLVANIA. The probability of choosing an N can be calculated as follows:

Probability of choosing an N = (Number of N's in the word) / (Total number of letters in the word)

Probability of choosing an N = 3 / 12

Probability of choosing an N = 1 / 4

Therefore, the probability of choosing an N is 1/4.

b. There are two A's in PENNSYLVANIA. The probability of choosing an A can be calculated as follows:

Probability of choosing an A = (Number of A's in the word) / (Total number of letters in the word)

Probability of choosing an A = 2 / 12

Probability of choosing an A = 1 / 6

Therefore, the probability of choosing an A is 1/6.

c. There is only one E in PENNSYLVANIA. The probability of choosing an E can be calculated as follows:

Probability of choosing an E = (Number of E's in the word) / (Total number of letters in the word)

Probability of choosing an E = 1 / 12

Therefore, the probability of choosing an E is 1/12.

Answer:

b i think let me know if im right

Step-by-step explanation:

Answer:

g(f(-3)) = 6.

Step-by-step explanation:

To obtain the value of f(-3), we must first determine g(f(-3)), which requires changing x in the expression for f(x) to -3:

f(x) = 2x^2 + 9x - 1

f(-3) = 2(-3)^2 + 9(-3) (-3) - 1\s= 2(9) (9) - 27 - 1\s= 18 - 27 - 1\s= -10

Knowing that f(-3) = -10 allows us to replace it in the expression for g(x):

g(x) = -x - 4

g(f(-3)) = g(-10) (-10)

Now, if we replace x in g(x) with -10, we obtain:

g(f(-3)) = g(-10) = -(-10) (-10) - 4 = 10 - 4 = 6

Hence, g(f(-3)) = 6.

Answer:

g(f(-3))=6

Step-by-step explanation:

To calculate g(f(-3)), we must first determine the value of f(-3), and then we must insert that value into g(x) to obtain the result.

By adding x = -3 to the formula for f(x), we may obtain f(-3).

f(-3) = 2(-3)

² + 9(-3) - 1

f(-3) = 2(9) - 27 - 1

f(-3) = 18 - 28

f(-3) = -10

Knowing that f(-3) = -10 allows us to replace it in the formula for g(x):

g(f(-3)) = g(-10) = -(-10) (-10) - 4 = 10 - 4 = 6

Hence, g(f(-3)) = 6.

S thus measures around 2.77 centimetres in length.

The law of sines is frequently used to find the elusive side or angle of a triangle. This law can be used if precise triangle measurement combinations are given. ASA The objective is to identify the unknown side given two angles and an included side.

The Law of Sines can be used to determine the length of side s: s/sin(mS) = q/sin(mQ).

replacing the specified values:

s/sin(10°) = 3.9/sin(74°)

s ≈ sin(10°) × 3.9 ÷ sin(74°)

s ≈ 0.684 × 3.9 ÷ 0.961

s ≈ 2.77 cm (rounded to the nearest 10th)

S thus measures around 2.77 centimetres in length.

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To find the equation of the drone's path, we can first find the coordinates of the center of the circle that the drone is flying around. We can do this by finding the midpoint between the two points the drone passes over:

Midpoint in the x-direction: (220 ft - 180 ft)/2 = 20 ft to the right of the origin.

Midpoint in the y-direction: (230 ft - 180 ft)/2 = 25 ft above the origin.

Therefore, the center of the circle is located at (20, 25) ft.

The radius of the circle can be found by calculating the distance between the center of the circle and either of the two points the drone passes over:

Radius: sqrt((20-(-180))^2 + (25-180)^2) = sqrt(40000 + 15625) = 205 ft (rounded to the nearest whole number)

So the equation for the drone's path is:

(x - 20)^2 + (y - 25)^2 = 205^2

To find how far north of Megan's position the drone is when it passes due north, we can substitute x = 0 into the equation:

(0 - 20)^2 + (y - 25)^2 = 205^2

400 + (y - 25)^2 = 42025

(y - 25)^2 = 41625

y - 25 = +/-sqrt(41625)

y = 25 +/- 204.06

So the drone is either 229.06 ft north or 22.94 ft south of Megan's position when it passes due north. Rounded to three decimal places, the answer is 229.06 ft north.

The ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

To determine if an ordered pair is a solution to two systems of equations, substitute the values ​​of the variables into each equation. If an ordered pair makes both equations true, it is the solution of the system. 

To find the ordered pair solutions for the system of equations, we need to solve the two equations simultaneously.

f(x) = x² + 1 ...(1)

f(x) = -x + 3 ...(2)

Setting the two equations equal to each other, we get:

x² + 1 = -x + 3

Rearranging this equation, we get:

x² + x - 2 = 0

Factoring this quadratic equation, we get:

(x + 2)(x - 1) = 0

Therefore, the solutions for x are x = -2 and x = 1.

Substituting these values of x into either equation (1) or (2), we get:

For x = -2: f(-2) = (-2)² + 1 = 5, and f(-2) = -(-2) + 3 = 5.

For x = 1: f(1) = 1² + 1 = 2, and f(1) = -1 + 3 = 2.

Therefore, the ordered pair solutions for the system of equations are (-2, 5) and (1, 2).

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Answer:

Roberto will pay a total of $525,654 for the house.

This problem involves finding the probability of an event (a student being absent) given that another event has already occurred (today is Friday). This is an example of conditional probability.

Therefore, the correct answer is A) conditional probability.

Answer:

A.

Step-by-step explanation:

This is a conditional probability. None of the other choices make sense, but the most distinct word is "given". This is a sure sign of a conditional probability, or Bayes Theorem. The condition A is that it is Friday. Event B is that a student is absent. P (A|B)

Answer:

Base=20m   height= 15m

Step-by-step explanation:

The area of a triangle is given by:

[tex]A=\frac{bh}{2}[/tex]

since base is 10 less than twice the height  b=2h-10

plugin in those values and knowing area is 150
[tex]150=[/tex][tex]\frac{h(2h-10)}{2}[/tex]

then solve for h

[tex]300=2h^2-10h[/tex] this is quadratic equation

[tex]h^2-5h-150=0[/tex]  
factorizing  (notice you can also use quadratic equation)

[tex](h-15)(h+10)=0[/tex]
which positive solution (height cant be negative) is h=15
then the base is b=2(15)-10=20

Answer:

The height is 15 meters and the base is 20 meters.

Step-by-step explanation:

Let's use the formula for the area of a right triangle:

A = (1/2)bh

Where A is the area, b is the base, and h is the height.

We're given that the area is 150 square meters, so we can substitute that in:

150 = (1/2)bh

Next, we're told that the base is 10 less than twice the height. In other words,

b = 2h - 10

We can substitute this expression for b into the equation for the area:

150 = (1/2)(2h - 10)h

Simplifying:

300 = (2h - 10)h

300 = 2h^2 - 10h

2h^2 - 10h - 300 = 0

Dividing both sides by 2:

h^2 - 5h - 150 = 0

Now we can solve for h using the quadratic formula:

h = (-(-5) ± sqrt((-5)^2 - 4(1)(-150))) / 2(1)

h = (5 ± sqrt(625)) / 2

h = (5 ± 25) / 2

We can ignore the negative root (which gives us a negative height), so:

h = 15

Now we can use the expression for b in terms of h to find the base:

b = 2h - 10

b = 2(15) - 10

b = 20

Therefore, the height is 15 meters and the base is 20 meters.

Answer:

the result of subtracting 1 and 1/2 from the sum of 4 and 2/3 and 5 and 2/5 is 257/30 = 8 and 39/40.

Step-by-step explanation:

To find the result of subtracting 1 and 1/2 from the sum of 4 and 2/3 and 5 and 2/5, we need to first add the two summands:

4 and 2/3 + 5 and 2/5

To add these mixed numbers, we first need to find a common denominator. The least common multiple of 3 and 5 is 15.

4 and 2/3 can be written as an improper fraction with denominator 3:

4 and 2/3 = 4 x 3/3 + 2/3 = 12/3 + 2/3 = 14/3

5 and 2/5 can be written as an improper fraction with denominator 5:

5 and 2/5 = 5 x 5/5 + 2/5 = 25/5 + 2/5 = 27/5

Now we can add the two fractions with a common denominator of 15:

14/3 + 27/5 = (14 x 5)/(3 x 5) + (27 x 3)/(5 x 3) = 70/15 + 81/15 = 151/15

So, the sum of 4 and 2/3 and 5 and 2/5 is 151/15.

Now we can subtract 1 and 1/2 from this sum:

151/15 - 1 1/2

To subtract mixed numbers, we first need to convert 1 and 1/2 to an improper fraction:

1 and 1/2 = 1 x 2/2 + 1/2 = 2/2 + 1/2 = 3/2

Now we can subtract the fractions with a common denominator of 15:

151/15 - 3/2 = (151 x 2)/(15 x 2) - (3 x 15)/(2 x 15) = 302/30 - 45/30 = 257/30

Therefore, the result of subtracting 1 and 1/2 from the sum of 4 and 2/3 and 5 and 2/5 is 257/30.

In response to the question, we may say that  Hence, 2 131/200 is the decimal mixed number in its most basic form.

The decimal number system is frequently used to express both integer and non-integer quantities. Non-integer values have been added to the Hindu-Arabic numeral system. The technique used to represent numbers in the decimal system is known as decimal notation. A decimal number consists of both a whole number and a fractional number. The numerical value of complete and partially whole quantities is expressed using decimal numbers, which are in between integers. The full number and the fractional part of a decimal number are separated by a decimal point. The decimal point is the little dot that appears between whole numbers and fractions. An example of a decimal number is 25.5.

We must separate the whole number and fraction components of 2.655 in order to change it into a mixed number. The integer portion of the decimal, which is 2 in this instance, represents the full number.

We take the total number and divide it by the decimal to determine the fractional portion.

2.655 - 2 = 0.655

The combined number is therefore 2 and 655/1000.

By dividing the numerator and denominator by their largest common factor, we may reduce the fraction to its simplest form and so make it easier to understand. The highest common factor between 655 and 1000 in this instance is 5.

655 ÷ 5 = 131

1000 ÷ 5 = 200

Hence, 2 131/200 is the mixed number in its most basic form.

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the value of 0.45 × 0.91 ÷ 0.0117 is 35.

Why it is and what is PEMDAS?

To find the value of 0.45 * 0.91 ÷ 0.0117, we can use the order of operations, which is also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction).

First, we need to perform the multiplication of 0.45 and 0.91:

0.45 ×0.91 = 0.4095

Then, we need to divide the result by 0.0117:

0.4095 ÷ 0.0117 = 35

Therefore, the value of 0.45 * 0.91 ÷ 0.0117 is 35.

PEMDAS is a mnemonic used to remember the order of operations in arithmetic and algebraic expressions. It stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

The order of operations is as follows:

Parentheses: Perform operations within parentheses first, working from the innermost set of parentheses to the outermost.

Exponents: Perform any calculations involving exponents, such as raising a number to a power or taking the square root.

Multiplication and Division: Perform multiplication and division in the order that they appear from left to right.

Addition and Subtraction: Perform addition and subtraction in the order that they appear from left to right.

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Answer:

2^7 or 128

Step-by-step explanation:

When we multiply two powers with the same base, we add their exponents. In this case, the base is 2 and the exponents are 3 and 4.

So, 2^3 • 2^4 can be simplified as:

2^3 • 2^4 = 2^(3+4) = 2^7

Therefore, 2^3 • 2^4 is equal to 128.

Answer:128

Step-by-step explanation:

i assume that by ^ you meant power,

2^3=2*2*2=8

2^4=2*2*2*2=16

8*16=128

The correct option is (a) ŷ = -1.34x+21.5 , that is the best model to fit the scatter plot.

A scatter plot (or scatter chart, scatter graph) uses dots to represent values for two(2) different numeric variables. The position of each dot on horizontal and vertical axis indicates values for an individual data point.

The model of the equation best for the plot is,

ŷ = -1.34x+21.5

At point (1,20),

ŷ  = -1.34x+21.5

20 = (-1.34 ×  1) + 21.5

20 ≈ 20.15

At point (3,19),

ŷ = -1.34x+21.5

19 = (-1.34 × 3) + 21.5

19 ≈17.45

At point (5,15),

ŷ = -1.34x+21.5

15 = (-1.34 × 5) + 21.5

15 ≈ 14.75

The model ŷ = -1.34x+21.5   is giving the best estimation.

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Answer:

120km/h

Step-by-step explanation:

Distance=14km

Time       =7m

A driver was fined for speeding in 100km/h

∴ we convert time into hours

Time =(7/60)h

Average speed of the car = total distance ÷total time

                                           =14km×60/7h=120km/h which is greater than                          

                                                                                                        100km/h

Answer:

11 11/12

Step-by-step explanation:

You can change these "mixed numbers" (a big whole numbers and also a fraction) to "improper fractions" (a single fraction with a bigger number on top and a smaller number on the bottom)

4 1/3 × 2 3/4

see image

13/3 × 11/4

Multiply straight across, top×top and bottom×bottom.

see image.

Change back to a mixed number by dividing.

The multiplication of 4 1/3 x 2 3/4 is 11 11/12.

The correct option is C.

A fraction that has the numerator higher than or equal to the denominator is said to be an improper fraction.

To multiply 4 1/3 and 2 3/4, we can first convert them to improper fractions:

4 1/3 = 13/3

2 3/4 = 11/4

Then we can multiply the fractions by multiplying the numerators and denominators separately:

(13/3) x (11/4) = (143/12)

Finally, we can convert the improper fraction back to a mixed number if desired:

143/12 = 11 11/12

Therefore, the answer is 11 11/12.

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The range, which is the distance between the smallest and greatest linear equation values in the data,  does not take into account the distribution of the data within that range.

In algebra, a linear equation refers to one with its form y=mx+b. B is the gradient, and m is the esta. The preceding clause is commonly referred to as a "linear function with two variables" so even though y and x are variables. Bivariate linear equations are linear equations with two variables. There are several linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation seems to have the structure y=mx+b, where m is the slope and b is the y-intercept, it is said to be linear. When a measurement seems to have the formula y=mx+b, both with m identifying its slope and b denoting the y-intercept, it is said to be linear.

Because it has a lower IQR, Fast Chicken can more consistently estimate their wait time (Interquartile Range). In this case, the IQR is the range of the middle 50% of the data, which is the distance between the first and third quartiles.

Super Fast Food, on the other hand, has a higher IQR, indicating that the data is more dispersed. This means that customers report a wider range of wait times, making it more difficult to estimate a consistent wait time. The range, which is the distance between the smallest and greatest values in the data, is not as useful for measuring consistency in this case because it does not take into account the distribution of the data within that range.

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Answer: The answer to this equation is In (252) + 5.

Step-by-step explanation:

To solve this equation, you will need to first apply the logarithm power identity.

Now evaluate the exponent.

5 + In (7) + In (6^2)

5 + In (7) + In (36)

Apply the logarithm power identity again to the rest of this equation.

5 + In (7) + In (36)

5 + In (7 x 36)

After that, simplify the expression.

-Multiply the numbers & rearrange the terms

5 + In(7 x 36)

In(252) + 5

Therefore, your answer for this equation would be In(252) + 5.

Alyssa Wagner

Middle School Srudent

Answer: Let's assume the two original numbers to be x and y.

If one of them is increased by 50%, then the new value will be 1.5x, and if the other one is decreased by 50%, the new value will be 0.5y.

The product of the two new numbers will be:

1.5x * 0.5y = 0.75xy

So, the new product is 0.75 times the original product. This means the product of the two numbers has decreased by 25%.

To summarize:

If one number is increased by 50% and the other number is decreased by 50%, the product of the two numbers will decrease by 25%.

The new product is 0.75 times the original product.

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